Prove that the relation 'is parallel to' on the set 'S' of all straight lines in a plane is an equivalence relation .
My attempt:
The relation 'is parallel to' on set 'S' is:
(1). Reflexive, because every line is parallel to itself.
2026-03-28 00:49:14.1774658954
Prove that the relation 'is parallel to' on the set 'S' of all straight lines in a plane is an equivalence relation
734 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ALGEBRA-PRECALCULUS
- How to show that $k < m_1+2$?
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Finding the value of cot 142.5°
- Why is the following $\frac{3^n}{3^{n+1}}$ equal to $\frac{1}{3}$?
- Extracting the S from formula
- Using trigonometric identities to simply the following expression $\tan\frac{\pi}{5} + 2\tan\frac{2\pi}{5}+ 4\cot\frac{4\pi}{5}=\cot\frac{\pi}{5}$
- Solving an equation involving binomial coefficients
- Is division inherently the last operation when using fraction notation or is the order of operation always PEMDAS?
- How is $\frac{\left(2\left(n+1\right)\right)!}{\left(n+1\right)!}\cdot \frac{n!}{\left(2n\right)!}$ simplified like that?
- How to solve algebraic equation
Related Questions in EQUIVALENCE-RELATIONS
- Relations of equivalence...
- Number of subsets, relations etc of a set
- Number of possible equivalence relations
- Why is $p(z) = \frac{e^z}{1 + e^z} \color{red}{\equiv} \frac{1}{1 + e^{-z}}$ and not $=$?
- Simple question about relations
- Total number of equivalence class for a set
- Is this an equivalence relation and explaination?
- Partition of a set identified by a equivalence relation
- Define an equivalence relation on $\{ 1,2,3,4 \}^2$ by: (, )(, ) if ⋅ = ⋅ . How many equivalence classes are there?
- Prove that $\sum_{i=1}^n\lvert[a_i]\rvert$ is even iff $n$ is even
Related Questions in SYMMETRY
- Do projective transforms preserve circle centres?
- Decomposing an arbitrary rank tensor into components with symmetries
- A closed manifold of negative Ricci curvature has no conformal vector fields
- Show, by means of an example, that the group of symmetries of a subset X of a Euclidean space is, in general, smaller than Sym(x).
- How many solutions are there if you draw 14 Crosses in a 6x6 Grid?
- Symmetry of the tetrahedron as a subgroup of the cube
- Number of unique integer coordinate points in an $n$- dimensional hyperbolic-edged tetrahedron
- The stretch factors of $A^T A$ are the eigenvalues of $A^T A$
- The square root of a positive semidefinite matrix
- Every conformal vector field on $\mathbb{R}^n$ is homothetic?
Related Questions in RELATIONS
- How are these definitions of continuous relations equivalent?
- Is a relation on which every element is related with itself alone transitive?
- Relation power composition
- Order relation proof
- Order relation proof ...
- How to identify if a given Hasse diagram is a lattice
- Is the relation < a strict total order?
- Is there a name for this property on a binary relation?
- Finding all reflexive binary relations of a set
- Showing that a relation is reflexive, symmetric and transitive
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?